View source: R/ZTNegativeBinomial.R
ZTNegativeBinomial | R Documentation |
Zero-truncated negative binomial distributions are frequently used to model counts where zero observations cannot occur or have been excluded.
ZTNegativeBinomial(mu, theta)
mu |
Location parameter of the negative binomial component of the distribution. Can be any positive number. |
theta |
Overdispersion parameter of the negative binomial component of the distribution. Can be any positive number. |
We recommend reading this documentation on https://alexpghayes.github.io/distributions3/, where the math will render with additional detail.
In the following, let X be a zero-truncated negative binomial random variable with parameter
mu
= μ.
Support: {1, 2, 3, ...}
Mean:
μ \cdot 1/(1 - F(0; μ, θ))
where F(k; μ, θ) is the c.d.f. of the NegativeBinomial
distribution.
Variance: m \cdot (μ + 1 - m), where m is the mean above.
Probability mass function (p.m.f.):
P(X = k) = f(k; μ, θ)/(1 - F(0; μ, θ))
where f(k; μ, θ) is the p.m.f. of the NegativeBinomial
distribution.
Cumulative distribution function (c.d.f.):
P(X = k) = F(k; μ, θ)/(1 - F(0; μ, θ))
Moment generating function (m.g.f.):
Omitted for now.
A ZTNegativeBinomial
object.
Other discrete distributions:
Bernoulli()
,
Binomial()
,
Categorical()
,
Geometric()
,
HurdleNegativeBinomial()
,
HurdlePoisson()
,
HyperGeometric()
,
Multinomial()
,
NegativeBinomial()
,
Poisson()
,
ZINegativeBinomial()
,
ZIPoisson()
,
ZTPoisson()
## set up a zero-truncated negative binomial distribution X <- ZTNegativeBinomial(mu = 2.5, theta = 1) X ## standard functions pdf(X, 0:8) cdf(X, 0:8) quantile(X, seq(0, 1, by = 0.25)) ## cdf() and quantile() are inverses for each other quantile(X, cdf(X, 3)) ## density visualization plot(0:8, pdf(X, 0:8), type = "h", lwd = 2) ## corresponding sample with histogram of empirical frequencies set.seed(0) x <- random(X, 500) hist(x, breaks = -1:max(x) + 0.5)
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